%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO637+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:15:34 AM UTC 2026
% Result : Theorem 72.23s 20.07s
% Output : CNFRefutation 72.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 35
% Syntax : Number of formulae : 157 ( 35 unt; 0 def)
% Number of atoms : 367 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 356 ( 146 ~; 144 |; 30 &)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 518 ( 46 sgn 177 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X0,X2,X1) ) ).
fof(ruleD2,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X1,X0,X2) ) ).
fof(ruleD3,axiom,
! [X0,X1,X2,X3] :
( ( coll(X0,X1,X3)
& coll(X0,X1,X2) )
=> coll(X2,X3,X0) ) ).
fof(ruleD7,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X0,X1,X3,X2) ) ).
fof(ruleD8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ) ).
fof(ruleD9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X2,X3,X4,X5)
& perp(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ) ).
fof(ruleD11,axiom,
! [X0,X1,X2] :
( midp(X2,X1,X0)
=> midp(X2,X0,X1) ) ).
fof(ruleD12,axiom,
! [X0,X1,X2,X3] :
( ( cong(X3,X0,X3,X2)
& cong(X3,X0,X3,X1) )
=> circle(X3,X0,X1,X2) ) ).
fof(ruleD13,axiom,
! [X0,X1,X2,X3,X4] :
( ( cong(X4,X0,X4,X3)
& cong(X4,X0,X4,X2)
& cong(X4,X0,X4,X1) )
=> cyclic(X0,X1,X2,X3) ) ).
fof(ruleD14,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X1,X3,X2) ) ).
fof(ruleD15,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X2,X1,X3) ) ).
fof(ruleD16,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X1,X0,X2,X3) ) ).
fof(ruleD18,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X1,X0,X2,X3,X4,X5,X6,X7) ) ).
fof(ruleD19,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ) ).
fof(ruleD20,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ) ).
fof(ruleD22,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
& eqangle(X0,X1,X2,X3,X4,X5,X6,X7) )
=> eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ) ).
fof(ruleD23,axiom,
! [X0,X1,X2,X3] :
( cong(X0,X1,X2,X3)
=> cong(X0,X1,X3,X2) ) ).
fof(ruleD24,axiom,
! [X0,X1,X2,X3] :
( cong(X0,X1,X2,X3)
=> cong(X2,X3,X0,X1) ) ).
fof(ruleD25,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( cong(X2,X3,X4,X5)
& cong(X0,X1,X2,X3) )
=> cong(X0,X1,X4,X5) ) ).
fof(ruleD39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ) ).
fof(ruleD40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ) ).
fof(ruleD41,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ) ).
fof(ruleD42b,axiom,
! [X0,X1,X2,X3] :
( ( coll(X2,X3,X1)
& eqangle(X2,X0,X2,X1,X3,X0,X3,X1) )
=> cyclic(X0,X1,X2,X3) ) ).
fof(ruleD43,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
& cyclic(X0,X1,X2,X5)
& cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X3) )
=> cong(X0,X1,X3,X4) ) ).
fof(ruleD45,axiom,
! [X0,X1,X2,X3,X4] :
( ( coll(X4,X0,X2)
& para(X3,X4,X1,X2)
& midp(X3,X0,X1) )
=> midp(X4,X0,X2) ) ).
fof(ruleD46,axiom,
! [X0,X1,X2] :
( cong(X2,X0,X2,X1)
=> eqangle(X2,X0,X0,X1,X0,X1,X2,X1) ) ).
fof(ruleD50,axiom,
! [X0,X1,X2,X3,X4] :
( ( midp(X4,X1,X2)
& circle(X3,X0,X1,X2) )
=> eqangle(X0,X1,X0,X2,X3,X1,X3,X4) ) ).
fof(ruleD51,axiom,
! [X0,X1,X2,X3,X4] :
( ( eqangle(X0,X1,X0,X2,X3,X1,X3,X4)
& coll(X4,X1,X2)
& circle(X3,X0,X1,X2) )
=> midp(X4,X1,X2) ) ).
fof(ruleD52,axiom,
! [X0,X1,X2,X3] :
( ( midp(X3,X0,X2)
& perp(X0,X1,X1,X2) )
=> cong(X0,X3,X1,X3) ) ).
fof(ruleD54,axiom,
! [X0,X1,X2,X3] :
( ( para(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X3) )
=> eqangle(X0,X3,X2,X3,X2,X3,X2,X1) ) ).
fof(ruleD55,axiom,
! [X0,X1,X2,X3] :
( ( perp(X3,X2,X0,X1)
& midp(X2,X0,X1) )
=> cong(X3,X0,X3,X1) ) ).
fof(ruleD66,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ) ).
fof(ruleD67,axiom,
! [X0,X1,X2] :
( ( coll(X0,X1,X2)
& cong(X0,X1,X0,X2) )
=> midp(X0,X1,X2) ) ).
fof(ruleD68,axiom,
! [X0,X1,X2] :
( midp(X0,X1,X2)
=> cong(X0,X1,X0,X2) ) ).
fof(exemplo6GDDFULL81109101,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( perp(X0,X3,X0,X6)
& perp(X2,X3,X2,X6)
& coll(X5,X0,X1)
& coll(X5,X3,X4)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2) )
=> cyclic(X0,X3,X6,X5) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( perp(X0,X3,X0,X6)
& perp(X2,X3,X2,X6)
& coll(X5,X0,X1)
& coll(X5,X3,X4)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2) )
=> cyclic(X0,X3,X6,X5) ),
inference(negate_conjecture,[status(cth)],[exemplo6GDDFULL81109101]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD1]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD2]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD3]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD7]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD8]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD9]) ).
cnf(c10,plain,
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD11]) ).
cnf(c11,plain,
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD12]) ).
cnf(c12,plain,
( cyclic(X1,X2,X3,X4)
| ~ cong(X0,X1,X0,X4)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD13]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD14]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD15]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD16]) ).
cnf(c17,plain,
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD18]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD19]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD20]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD22]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD23]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD24]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD25]) ).
cnf(c38,plain,
( para(X0,X1,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(clausification,[status(esa)],[ruleD39]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD40]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD41]) ).
cnf(c42,plain,
( cyclic(X1,X2,X0,X3)
| ~ coll(X0,X3,X2)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(clausification,[status(esa)],[ruleD42b]) ).
cnf(c43,plain,
( ~ eqangle(X2,X0,X2,X1,X5,X4,X5,X3)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| cong(X0,X1,X4,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD43]) ).
cnf(c45,plain,
( midp(X3,X1,X4)
| ~ coll(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD45]) ).
cnf(c46,plain,
( eqangle(X0,X1,X1,X2,X1,X2,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD46]) ).
cnf(c50,plain,
( eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ midp(X4,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD50]) ).
cnf(c51,plain,
( midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ coll(X4,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD51]) ).
cnf(c52,plain,
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(clausification,[status(esa)],[ruleD52]) ).
cnf(c54,plain,
( eqangle(X0,X3,X2,X3,X2,X3,X2,X1)
| ~ para(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD54]) ).
cnf(c55,plain,
( cong(X3,X1,X3,X2)
| ~ perp(X3,X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD55]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD66]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD67]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD68]) ).
cnf(c117,plain,
perp(sK524,sK525,sK524,sK528),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c118,plain,
perp(sK522,sK525,sK522,sK528),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c119,plain,
~ cyclic(sK522,sK525,sK528,sK527),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( cyclic(X1,X3,X4,X2)
| ~ cong(X0,X1,X0,X4)
| ~ cong(X0,X1,X0,X3)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c12]) ).
cnf(d1,plain,
perp(sK522,sK528,sK522,sK525),
inference(resolution,[status(thm)],[c118,c7]) ).
cnf(d2,plain,
perp(sK522,sK528,sK525,sK522),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( cong(sK522,sK525,sK522,sK522)
| ~ midp(sK528,sK525,sK522) ),
inference(resolution,[status(thm)],[c55,d2]) ).
cnf(d4,plain,
( cong(sK522,sK522,sK522,sK525)
| ~ midp(sK528,sK525,sK522) ),
inference(resolution,[status(thm)],[d3,c23]) ).
cnf(d5,plain,
( cyclic(sK522,sK525,X1,X0)
| ~ cong(sK522,sK522,sK522,X1)
| ~ midp(sK522,sK522,X0)
| ~ midp(sK528,sK525,sK522) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
perp(sK524,sK528,sK524,sK525),
inference(resolution,[status(thm)],[c117,c7]) ).
cnf(d7,plain,
( ~ perp(X0,X1,sK524,sK528)
| para(X0,X1,sK524,sK525) ),
inference(resolution,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
para(sK524,sK525,sK524,sK525),
inference(resolution,[status(thm)],[d7,c117]) ).
cnf(d9,plain,
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c18]) ).
cnf(d10,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d9,c38]) ).
cnf(d11,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[d11,c66]) ).
cnf(d13,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
( ~ coll(X2,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[d14,d15]) ).
cnf(d17,plain,
( ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d16,c67]) ).
cnf(d18,plain,
( eqangle(X3,X0,X3,X1,X2,X0,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c19]) ).
cnf(d19,plain,
( eqangle(X0,X3,X3,X1,X2,X0,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d18,c17]) ).
cnf(d20,plain,
( ~ cyclic(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X0,X2)
| ~ cyclic(X0,X1,X0,X0)
| cong(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[d19,c43]) ).
cnf(d21,plain,
( ~ para(X0,X2,X0,X2)
| cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[c42,c39]) ).
cnf(d22,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d11,d21]) ).
cnf(d23,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[d16,d22]) ).
cnf(d24,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d23,c14]) ).
cnf(d25,plain,
cyclic(X0,X1,X2,X0),
inference(resolution,[status(thm)],[d24,c15]) ).
cnf(d26,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d25,c13]) ).
cnf(d27,plain,
( ~ cyclic(X0,X1,X0,X0)
| ~ cyclic(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d26,d20]) ).
cnf(d28,plain,
( ~ cyclic(X0,X1,X0,X0)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d24,d27]) ).
cnf(d29,plain,
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d23,d28]) ).
cnf(d30,plain,
cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d25,d29]) ).
cnf(d31,plain,
midp(X0,X1,X1),
inference(resolution,[status(thm)],[d30,d17]) ).
cnf(d32,plain,
( ~ midp(X2,X1,X2)
| midp(X0,X1,X0)
| ~ coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[d11,c45]) ).
cnf(d33,plain,
( midp(X2,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d16,d32]) ).
cnf(d34,plain,
midp(X0,X1,X0),
inference(resolution,[status(thm)],[d33,d31]) ).
cnf(d35,plain,
midp(X0,X0,X1),
inference(resolution,[status(thm)],[d34,c10]) ).
cnf(d36,plain,
( cyclic(sK522,sK525,X0,X1)
| ~ cong(sK522,sK522,sK522,X0)
| ~ midp(sK528,sK525,sK522) ),
inference(resolution,[status(thm)],[d35,d5]) ).
cnf(d37,plain,
( eqangle(X4,X1,X4,X2,X5,X6,X7,X8)
| ~ eqangle(X3,X1,X3,X0,X5,X6,X7,X8)
| ~ circle(X3,X4,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c50,c21]) ).
cnf(d38,plain,
( eqangle(X3,X0,X2,X3,X2,X3,X2,X1)
| ~ cyclic(X0,X1,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c54,c17]) ).
cnf(d39,plain,
( eqangle(X4,X0,X4,X3,X2,X2,X2,X1)
| ~ circle(X2,X4,X0,X3)
| ~ midp(X2,X0,X3)
| ~ cyclic(X0,X1,X2,X2)
| ~ para(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[d38,d37]) ).
cnf(d40,plain,
( ~ circle(X0,X3,X0,X2)
| midp(X1,X0,X2)
| ~ coll(X1,X0,X2)
| ~ cyclic(X0,X1,X0,X0)
| ~ circle(X0,X3,X0,X2)
| ~ midp(X0,X0,X2)
| ~ para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d39,c51]) ).
cnf(d41,plain,
( ~ circle(X1,X3,X1,X2)
| ~ midp(X1,X1,X2)
| midp(X0,X1,X2)
| ~ para(X1,X0,X1,X1)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d26,d40]) ).
cnf(d42,plain,
( ~ circle(X0,X3,X0,X2)
| midp(X1,X0,X2)
| ~ midp(X0,X0,X2)
| ~ para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d16,d41]) ).
cnf(d43,plain,
( cong(X0,X2,X0,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c23]) ).
cnf(d44,plain,
( eqangle(X1,X2,X0,X2,X0,X1,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[c46,c19]) ).
cnf(d45,plain,
( para(X0,X1,X0,X0)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[d44,c38]) ).
cnf(d46,plain,
( ~ midp(X0,X1,X0)
| para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d45,d43]) ).
cnf(d47,plain,
para(X0,X1,X0,X0),
inference(resolution,[status(thm)],[d34,d46]) ).
cnf(d48,plain,
( ~ circle(X1,X3,X1,X2)
| ~ midp(X1,X1,X2)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d47,d42]) ).
cnf(d49,plain,
( ~ circle(X1,X3,X1,X2)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d35,d48]) ).
cnf(d50,plain,
( circle(X0,X1,X3,X2)
| ~ cong(X0,X1,X0,X3)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c11]) ).
cnf(d51,plain,
( cong(sK522,sK522,sK522,sK528)
| ~ midp(sK525,sK522,sK528) ),
inference(resolution,[status(thm)],[c55,c118]) ).
cnf(d52,plain,
( cong(sK522,sK528,sK522,sK522)
| ~ midp(sK525,sK522,sK528) ),
inference(resolution,[status(thm)],[d51,c23]) ).
cnf(d53,plain,
( circle(sK522,sK528,sK522,X0)
| ~ midp(sK522,sK528,X0)
| ~ midp(sK525,sK522,sK528) ),
inference(resolution,[status(thm)],[d52,d50]) ).
cnf(d54,plain,
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[c46,c38]) ).
cnf(d55,plain,
( para(sK522,sK522,sK522,sK528)
| ~ midp(sK525,sK522,sK528) ),
inference(resolution,[status(thm)],[d51,d54]) ).
cnf(d56,plain,
( ~ midp(sK522,X0,sK522)
| midp(sK522,X0,sK528)
| ~ coll(sK522,X0,sK528)
| ~ midp(sK525,sK522,sK528) ),
inference(resolution,[status(thm)],[d55,c45]) ).
cnf(d57,plain,
( midp(sK522,X0,sK528)
| ~ midp(sK522,X0,sK522)
| ~ midp(sK525,sK522,sK528) ),
inference(resolution,[status(thm)],[d16,d56]) ).
cnf(d58,plain,
( midp(sK522,X0,sK528)
| ~ midp(sK525,sK522,sK528) ),
inference(resolution,[status(thm)],[d34,d57]) ).
cnf(d59,plain,
cong(X0,X1,X1,X0),
inference(resolution,[status(thm)],[d30,c22]) ).
cnf(d60,plain,
perp(sK522,sK525,sK528,sK522),
inference(resolution,[status(thm)],[c118,c6]) ).
cnf(d61,plain,
perp(sK528,sK522,sK522,sK525),
inference(resolution,[status(thm)],[d60,c7]) ).
cnf(d62,plain,
( cong(sK528,X0,sK522,X0)
| ~ midp(X0,sK528,sK525) ),
inference(resolution,[status(thm)],[c52,d61]) ).
cnf(d63,plain,
( cong(sK528,X0,X0,sK522)
| ~ midp(X0,sK528,sK525) ),
inference(resolution,[status(thm)],[d62,c22]) ).
cnf(d64,plain,
( circle(sK528,sK528,X0,sK522)
| ~ cong(sK528,sK528,sK528,X0)
| ~ midp(sK528,sK528,sK525) ),
inference(resolution,[status(thm)],[d63,c11]) ).
cnf(d65,plain,
( circle(sK528,sK528,X0,sK522)
| ~ cong(sK528,sK528,sK528,X0) ),
inference(resolution,[status(thm)],[d35,d64]) ).
cnf(d66,plain,
circle(sK528,sK528,sK528,sK522),
inference(resolution,[status(thm)],[d65,d59]) ).
cnf(d67,plain,
midp(X0,sK528,sK522),
inference(resolution,[status(thm)],[d49,d66]) ).
cnf(d68,plain,
midp(X0,sK522,sK528),
inference(resolution,[status(thm)],[d67,c10]) ).
cnf(d69,plain,
midp(sK522,X0,sK528),
inference(resolution,[status(thm)],[d68,d58]) ).
cnf(d70,plain,
midp(sK522,sK528,X0),
inference(resolution,[status(thm)],[d69,c10]) ).
cnf(d71,plain,
( circle(sK522,sK528,sK522,X0)
| ~ midp(sK525,sK522,sK528) ),
inference(resolution,[status(thm)],[d70,d53]) ).
cnf(d72,plain,
circle(sK522,sK528,sK522,X0),
inference(resolution,[status(thm)],[d68,d71]) ).
cnf(d73,plain,
midp(X0,sK522,X1),
inference(resolution,[status(thm)],[d72,d49]) ).
cnf(d74,plain,
midp(X0,X1,sK522),
inference(resolution,[status(thm)],[d73,c10]) ).
cnf(d75,plain,
( cyclic(sK522,sK525,X0,X1)
| ~ cong(sK522,sK522,sK522,X0) ),
inference(resolution,[status(thm)],[d74,d36]) ).
cnf(d76,plain,
( ~ cong(X3,X4,X0,X1)
| cong(X3,X4,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c24]) ).
cnf(d77,plain,
( cong(sK522,sK528,sK522,sK522)
| ~ midp(sK525,sK528,sK522) ),
inference(resolution,[status(thm)],[c55,d60]) ).
cnf(d78,plain,
( cong(sK522,sK522,sK522,sK528)
| ~ midp(sK525,sK528,sK522) ),
inference(resolution,[status(thm)],[d77,c23]) ).
cnf(d79,plain,
( cong(sK522,sK522,sK522,X0)
| ~ midp(sK522,sK528,X0)
| ~ midp(sK525,sK528,sK522) ),
inference(resolution,[status(thm)],[d78,d76]) ).
cnf(d80,plain,
( cong(sK522,sK522,sK522,X0)
| ~ midp(sK525,sK528,sK522) ),
inference(resolution,[status(thm)],[d70,d79]) ).
cnf(d81,plain,
cong(sK522,sK522,sK522,X0),
inference(resolution,[status(thm)],[d74,d80]) ).
cnf(d82,plain,
cyclic(sK522,sK525,X0,X1),
inference(resolution,[status(thm)],[d81,d75]) ).
cnf(d83,plain,
$false,
inference(resolution,[status(thm)],[d82,c119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO637+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n018.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 13:48:22 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 72.23/20.07 % SZS status Theorem for theBenchmark.p
% 72.23/20.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------